Abstract
In order to explore further the underlying mechanism of the scale-free networks, we study stochastic secession as a mechanism for the creation of complex networks. In this evolution the network growth incorporates the addition of new links between existing nodes, the deleting and rewiring of some existing links, and the stochastic secession of nodes. To random growing networks with preferential attachment, the model yields scale-free behavior for the degree distribution. Furthermore, we get the analytical expression of the power law degree distribution with scaling exponent γ ranges from 1.1 to 9. The analytical expressions are in good agreement with the numerical simulation results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Strogatz, S.H.: Exploring complex networks. Nature 410, 268–276 (2001)
Albert, R., Barabási, A.L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of networks. Adv. Phys. 51, 1079–1187 (2002)
Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45, 167–256 (2003)
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Structure and Dynamics of Complex Networks. Phys. Rep. 424, 175 (2006)
Seyed-allaei, H., Bianconi, G., Marsili, M.: Scale-free networks with an exponent less than two. Phys. Rev. E 73 (2006)
Albert, R., Barabási, A.L.: Topology of Evolving Networks: Local Events and Universality. Phys. Rev. Lett. 85, 5234–5237 (2000)
Chen, Q.H., Shi, D.H.: The modeling of scale-free networks. Physica A 335, 240 (2004)
Geng, X.M., Li, Q.: Random Models of Scale-Free Networks. Physica A 356, 554 (2004)
Gnutella network is an application that runs on a personal computer and shares files with other users across the Internet. The networks work by connecting individual computers together to share files instead of having to go through a central server
Jovanovic, M., Annexstein, F., Berman, K.: Tech. Rep., University of Cincinnati (2001), http://www.ececs.uc.edu/~annexste/Papers/scalabilityissues.ps
Ebel, H., Mielsch, L.I., Bornholdt, S.: Scale-free topology of e-mail networks. Phys. Rev. E 66, 035103 (2002)
Toroczkai, Z., Bassler, K.: Jamming is limited in scale-free systems. Nature 428, 716 (2004)
Dunne, J.A., Williams, R.J., Martinez, N.D.: Food-web structure and network theory: The role of connectance and size. Pro. Natl. Acad. Sci. USA 99, 12917 (2002)
Newman, M.E.J.: Scientific collaboration networks. I. Network construction and fundamental results. Phys. Rev. E 64, 016131 (2001)
Newman, M.E.J.: Mixing patterns in networks. Phys. Rev. E, 67, 026126 (2003)
Valverde, S., Solé, R.V.: Hierarchical Small Worlds in Software Architecture, e-print: cond-mat/0307278
Montoya, J.M., Solé, R.V.: Small World Patterns in Food Webs. J. Theor. Biol. 214, 405–412 (2002)
Camacho, J., Guimerà, R., Amaral, L.A.N.: Robust Patterns in Food Web Structure. Phys. Rev. Lett. 88, 228102 (2002)
Amaral, L.A.N., Scala, A., Barthélémy, M., Stanley, H.E.: Classes of small-world networks. Pro. Natl. Acad. Sci. USA 97, 11149 (2000)
Lawrence, S., Giles, C.L.: Searching the World Wide Web. Science 280, 98–100 (1998)
Huberman, B.A., Adamic, L.A.: Internet: Growth dynamics of the World-Wide Web. Nature 406, 131 (1999)
Vázquez, A., Pastor-Satorras, R., Vespignani, A.: Large-scale topological and dynamical properties of the Internet. Pres. Rev. E 65, 066130 (2002)
Chung, F., Lu, L.: Coupling Online and Offline Analyses for Random Power Law Graphs. Internet Math. 1, 409–461 (2004)
Cooper, C., Frieze, A., Vera, J.: Random Deletion in a Scale-Free Random Graph Process. Internet Math. 1, 463–483 (2004)
Cheng, G.R., Fan, Z.P., Li, X.: Modelling the complex Internet topology. In: Vattay, G., Kocarev, L. (eds.) Complex Dynamics in Communication Networks, pp. 213–235. Springer, Heidelberg (2005)
Goh, K.-I., Kahng, B., Kim, D.: Fluctuation-Driven Dynamics of the Internet Topology. Phys. Rev. Lett. 88, 108701 (2002)
Chen, Q., Chang, H., Govindan, R., Jamin, S.: The origin of power laws in Internet topologies revisited. In: Proceedings of the 21st Annual Joint Conference of the IEEE Computer and Communications Societies, pp. 608–617. IEEE Computer Society, Los Alamitos (Silver Spring 2002)
Deng, K., Zhao, H.P., Li, D.J.: Statistical Mechanics and its Applications. Physica A 379, 714 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Geng, XM., Wen, GH., Wan, SC., Xiong, JY. (2009). Emergence of Scale-Free Networks with Seceding Mechanism. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02469-6_74
Download citation
DOI: https://doi.org/10.1007/978-3-642-02469-6_74
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02468-9
Online ISBN: 978-3-642-02469-6
eBook Packages: Computer ScienceComputer Science (R0)